In the News (Fri 9 Dec 16)

Penrose began to work on the problem of whether a set of shapes could be found which would tile a surface but without generating a repeating pattern (known as quasi-symmetry).

Penrose was raised in a family with strong mathematical interests: his mother was a doctor, his father, a medical geneticist, used math in his work as well as his recreation, one brother is a mathematician, another was ten times British chess champion.

Roger and his father are the creators of the famous Penrosestaircase and the impossible triangle known as the tribar.

Penrose suspects that a greater understanding of the functioning of the human brain may depend on a fundamentally new understanding of physics, to be sought in a radical new theory of quantum gravity.

Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the University of Oxford.

Penrose and Stuart Hameroff have constructed a theory in which human consciousness is the result of quantum gravity effects in microtubules.

www.bookrags.com /Roger_Penrose (5262 words)

From quasicrystals to Kleenex(Site not responding. Last check: 2007-10-18)

Penrose, who was knighted in 1994 for his services to science, is best known for his work on relativity theory and quantum mechanics, having shared the 1988 Wolf Prize for Physics with Stephen Hawking.

Penrose first developed a set of six tiles in 1973 and then "began thinking about reducing the number; and by various operations of slicing and re-gluing, I was able to reduce it to two".

Penrose tilings have also been put to rather different use: in 1997, Kleenex used a form of the rhomb design on their quilted toilet paper.

The Penrose stairs is an impossible object devised by Lionel Penrose and his son Roger Penrose and can be seen as a variation on his Penrose triangle.

It is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher.

The staircase had also been discovered previously by the Swedish artist Oscar Reutersvärd, but neither Penrose nor Escher were aware of his designs.

Penrose sees that he has no hope of overthrowing the case for strong AI unless he can dislodge one of the most imperturbable objects in the intellectual universe: something I will call the Cathedral of Science.

Penrose neglects to provide any argument to show what those limits are, and this is surprising, since this is where most of the attention is focussed in artificial intelligence today.

I may well have missed a crucial ingredient in Penrose's argument that somehow obviates this criticism, but it is disconcerting that he does not even address the issue, and often writes as if an algorithm could have only the powers it could be proven mathematically to have in the worst case.

Penrose points out that there is a contradiction in the entropy increase picture of the big bang, which is that the background radiation matches a model that is in thermal equilibrium.

Penrose suggested his Weyl curvature hypothesis in 1979 as a physical origin of the increasing entropy of the universe with time.

Penrose argues that the appropriate conformally invariant verion of general relativity the spin-2 field picks up an inverse conformal factor when the conformal tranformation is applied to the metrc, while the Weyl curvature does not.

ppcook.blogspot.com /2006/09/penrose-universe.html (2757 words)

Roger Penrose: A Knight on the tiles(Site not responding. Last check: 2007-10-18)

Penrose is unusual in believing that quantum mechanics will have to change in order to fit into such a unified theory.

Penrose's ideas on consciousness are, to say the least, controversial in the AI community.

Penrose shows himself an unabashed realist, by proclaiming that acting conscious is not the same as being conscious.

The argument Penrose unfolds has more facets than my summary can report, and it is unlikely that such an enterprise would succumb to a single, crashing oversight on the part of its creator--that the argument could be "refuted" by any simple objection.

And Penrose then goes to some length to argue that there could be no algorithm, or at any rate no practical algorithm, for insight.

I was struck as never before by the gleeful staircase of human artifices--diagrams, mappings, formalisms--piled one on top of the other over the years, permitting our species so much as to entertain such audacious hypotheses about the world we live in.

Penrose tilings are well known because of their interesting and sometimes intriguing properties; for example, they are locally but not globally symmetric under 5-fold rotations, quasi-periodic with respect to translations, self-similar, and more.

Now we project the staircase perpendicularly onto E. Adjacent edges of the staircase collapse to adjacent line segments in E. We have as result a tiling of this one-dimensional space.

In the background is a Penrose tiling, which is the projection of the surface onto the generating plane E (see the previous section).

The visual aspect of Penrose's creativity is well-known: the Penrosestaircase, which he invented in collaboration with his father, is a fascinating perceptual puzzle, while the Penrose tiling is a mesmeric solution to a long-standing geometric problem.

Penrose's sketches gave form to mathematical and physical concepts, from the five elements and their corresponding Platonic solids, to light cones and spin states, and in doing so allowed the audience to glimpse a great theorist's vision of the mathematical world.

Professor Sir Roger Penrose, FRS OM, is Emeritus Rouse Ball Professor of the University of Oxford.

Our plan was to assemble a multidisciplinary and international group of geologists and geophysicists to first characterize the geologic and seismic signature of active transition areas around the world and then to compare and contrast these characteristics to ancient transitions described from mountain belts.

Strain partitioning, or the manifestation of transpressional plate motion into parallel and coeval systems of strike-slip and thrust faults, has been the topic of earlier Penrose Conferences and was addressed again at this session because of the common occurrence of transpressional suites of structures in all three types of transition area.

The Penrose participants shared their impressions of seismic hazard issues to the visitors based on their experiences in this and other transition areas.

www.geosociety.org /penrose/99pcrpt1.htm (3477 words)

WHEN - History(Site not responding. Last check: 2007-10-18)

The monks in the picture seem to be either forever ascending or descending the impossible staircase that leads to nowhere.

This idea of the impossible staircase was not discovered by Escher himself, but its use in “Ascending and Descending” was actually inspired by the actual founders, Roger Penrose and his father Lionel.

Both the triangle and staircase are conceptually impossible, which was what obviously peaked Escher’s interest after these discoveries were published in the British Journal of Psychology in 1958.

ahsmail.uwaterloo.ca /~mgramsda/when.html (186 words)

Our City's Voice: The Gazette's First 125 Years(Site not responding. Last check: 2007-10-18)

Although Penrose was accused of using a raised ``a'' in the hotel's logo to belittle the competing Antlers Hotel, he insisted it was only to add a distinguishing touch to the name Broadmoor, which couldn't be copyrighted.

The superb decorative achievements in the lobby, the grand staircase and the vaulted vestibule above never failed to bring gasps of admiration.

Penrose, the work will not be considered complete until the Broadmoor hotel has been accepted as the greatest tourist hotel in America.''

Roger Penrose (the British mathematician) described the second type—impossible perspectives—as being “rather than locally unambiguous, but globally impossible, they are everywhere locally ambiguous, yet globally impossible” (Quoted from Coxeter, 154).

This basis for this idea is not Escher’s—he found this (along with the staircase) in an article by Roger Penrose and his son, L.S. Penrose, in 1958 (Ernst, quoted in Coxeter 125).

The tribar, or Roger Penrose’s triangle, is formed of three rectangular beams.

www.123helpme.com /view.asp?id=28639 (2212 words)

Penrose stairway(Site not responding. Last check: 2007-10-18)

An impossible figure named after by the British geneticist Lionel Penrose (1898-1972), father of Roger Penrose.

It served as an inspiration for the staircase in M. Escher's famous print "Ascending and Descending." Although the Penrose stairway cannot be realized in three dimensions, this impossibility is not immediately perceived and, in fact, the paradox is not even apparent to many people at a quick glance.

Although Escher and the Penroses made the Stairway famous, it was, unbeknownst to them, independently discovered and refined years before by the Swedish artist Oscar Reutersvard.

A year round Christmas tree decorated with roses, cherubs and bows takes it's place in one corner while an exquisite staircase showcasing antique family photographs leads the way to the guest rooms in the other corner.

Penrose Inn offers relaxation as well as an inviting array of things to do.

The lithograph depicts a large building roofed by a never-ending staircase.

Two figures sit apart from the people on the endless staircase: one in a secluded courtyard, the other on a lower set of stairs.

Ascending and Descending was influenced by, and is an artistic implementation of, the Penrose stairs, an impossible object; Lionel Penrose had first published his concept in the February, 1958 issue of the British Journal of Psychology.

en.wikipedia.org /wiki/Ascending_and_Descending (230 words)

Ascending and Descending(Site not responding. Last check: 2007-10-18)

The graphic below shows the original Penrose drawing on the left and a sliced version of it on the right, which shows how the deception was accomplished.

It can be seen that the staircase is in a horizontal plane, while the sections lie in a spiral.

This is why slice #1 starts at the upper left and ends up in the lower left, instead of staying in the same horizontal plane.

britton.disted.camosun.bc.ca /jbimpstair.htm (158 words)

Tim Bahls(Site not responding. Last check: 2007-10-18)

Roger Penrose (the British mathematician) described the second type—impossible perspectives—as being “rather than locally unambiguous, but globally impossible, they are everywhere locally ambiguous, yet globally impossible” (Quoted from Coxeter, 154).

This basis for this idea is not Escher’s—he found this (along with the staircase) in an article by Roger Penrose and his son, L.S. Penrose, in 1958 (Ernst, quoted in Coxeter 125).

h is pushing the staircase up on the page, while I want the stair case to meet itself.